For 𝑑𝑦𝑑𝑡+𝑝(𝑡)𝑦(𝑡)=𝑔(𝑡) consider a 𝜇(𝑡) that 𝜇𝑑𝑦𝑑𝑡+𝜇𝑝(𝑡)𝑦(𝑡)=𝜇𝑔(𝑡) take 𝑑𝜇𝑑𝑡=𝜇𝑝(𝑡)⟹𝜇=𝐶𝑒𝑝(𝑡)𝑡 therefore, we can turn the equation above to 𝑑𝑑𝑡(𝜇𝑦)=𝜇𝑔(𝑡)⟹𝑦=∫𝜇𝑔(𝑡)𝑑𝑡+𝐶𝜇 then plug 𝑚𝑢 in as the solution.